Re: [Maxima-discuss] simplify_sum leads to a wrong value

[Raymond T. <toy...@gm...>]

>>>>> "philippe" == philippe  <rou...@gm...> writes:

    philippe> Hi,
    philippe> I've check the results with SAgeMath (which obviously call maxima for
    philippe> this computation) and wolframalpha. This last one found another closed
    philippe> form for the series :

    philippe> https://photos.app.goo.gl/XGoyMm9TCa6t34gs7

Interesting.  Maxima can simplify the 2F1 function:

hgfred([1/2,2],[5/2],x);
(sqrt(x)*(3*atanh(sqrt(x))*x+3*atanh(sqrt(x)))-3*x)/(4*x^2)$

If you evaluate this at x = -(-1)^(2/3) and x = (-1)^(1/3) you get 3/4
for both.  Which is pretty obvious since (-1)^(1/3) = -1 and
-(-1)^(2/3) = -1, assuming principal roots.  This gives

((-1)^(1/6)-(-1)^(5/6))/8 = 0.2165063509461097

Which matches neither your expected result nor maxima's simplify_sum result.

It's not clear which of the three roots should be used in the
formula.  

Wolfram Alpha gives the same simplified result that hgfred does, so at
least that's not to blame.